The convergence of the biomedical revolution and the information technology revolution is a major event in the history of science. The emerging discipline of Computational Biology is a natural result of this convergence. The mathematical and computational sciences lie at the center of this new endeavor, providing the tools and framework for model building and quantitative analysis. The main focus of our proposed center is on the brain, and specifically on neuroimaging. This area has a long tradition of sophisticated mathematical and computational techniques. Nevertheless, new developments in related areas of mathematics and computational science have emerged in recent years, some from related application areas such as Computer Graphics, Computer Vision, and Image Processing, as well as from Computational Mathematics and the Computational Sciences. We are confident that many of these ideas can be applied beneficially to neuroimaging. During our planning grant, we developed a broad range of new, interdisciplinary collaborations and a strong track record of productivity across the continuum of mathematics, computer science, and neuroscience. Pressing problems in brain mapping and neuroimaging present exciting challenges and opportunities for mathematicians and computational scientists. In this Core, we describe some of the mathematical and computational techniques that we believe will be relevant. These include an extensive set of computational and biomedical advances that resulted from two years of collaborative work during our planning grant.